A meteor shower is the result of an interaction between a planet, such as Earth, and streams of debris from a comet.
Where we run into a problem with getting close to a freshly passed comet is that it increases the odds of us suddenly bumping into a recently left larger chunk of debris with little notice.
As burdman and others have already mentioned, the danger to the ISS is due to its lack of atmospheric protection from even smaller debris. Most of that would simply burn up in our atmosphere and create a spectacular meteor shower, but to the ISS it would be the equivalent of hitting it with a high-powered sandblaster.
BTW, those calculating the distance in AU’s need to remember that those distances are measured from the center of each body. So that is the distance from the core of the comet to the core of the earth. To find the actual passing distance you also need to subtract the distance to each objects surface and the distance from the surface to the edge of its atmosphere.
edit on 4/15/2011 by defcon5 because: (no reason given)